A Local Structure Graph Model: Modeling Formation of Network Edges as a Function of Other Edges

Localized network processes are central to the study of political science, whether in the formation of political coalitions and voting blocs, balancing and bandwagoning, policy learning, imitation, diffusion, tipping-point dynamics, or cascade effects. These types of processes are not easily modeled using traditional network approaches, which focus on global rather than local structures within networks. We show that localized network processes, in which network edges form in response to the formation of other edges, are best modeled by shifting from the traditional theoretical framework of nodes-as-actors to what we term a nodes-as-actions framework, which allows for zeroing in on relationships among network connections. We show that the proposed theoretical framework is statistically compatible with a local structure graph model (LSGM). We demonstrate the properties of LSGMs using a Monte Carlo experiment and explore action–reaction processes in two empirical applications: formation of alliances among countries and legislative cosponsorships in the US Senate.